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If a * b = ab + a + b, draw the graph of y = 3 * x + 1 * 2.

Telecom operators get revenue from transfer of data and voice. Average revenue received from transfer of each unit of data is called ARDT. In the diagram below, the revenue received from data transfer as percentage of total revenue received and the ARDT in US Dollars (USD) are given for various countries.

It is expected that by 2010, revenue from data transfer as a percentage of total revenue will triple in India and double for Sweden. Assume that in 2010, the total revenue in India is twice that of Sweden and that the volume of data transfer is the same in both the countries. What is the percentage increase in ARDT in India if there is no change in ARDT in Sweden?

Q18. Count the number of triangles in the following figure.

Question 86

Babita bought 160 kg of mangoes at Rs. 48 per kg. She sold 70 $\%$ of the mangoes at Rs. 70 per kg and the remaining mangoes at Rs. 40 per kg. Find Babita's gain or loss percent on the whole dealing.

How many bronze medals did college R win in these five events?

The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC.
In any round of voting, the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event.
A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities (s) he voted for in earlier rounds are out of contention in that round of voting.)
A member is also ineligible to cast a vote in a round if the city (s)he represents is in contention in that round of voting.
As long as the member is eligible, (s)he must vote and vote for only one candidate city in any round of voting.
The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds.

It is also known that:

* All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well.
* Those who voted for New York in round 1, voted either for Beijing or Paris in round 2.
* The difference in votes cast for the two contending cities in the last round was 1.
* 50% of those who voted for Beijing in round 1, voted for Paris in round 3.

Which of the following statements must be true?
1) IOC member from New York must have voted for Paris in round 2.
2) IOC member from Beijing voted for London on round 3.

Two concentric circles are of radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.

If a,b,c are the roots of the equation $x^3-4x+24=0$, then the equation whose roots are b+c, c+a and a+b is given by:

Why did the opposition claim the election as unconstitutional?

Select the correct code:

Study the following information carefully and answer the given questions:
A word and number arrangement machine when given an input line of words and numbers rearranges them following a particular rule in each step. The following is an illustration of the input and the rearrangement which the machine follows. (All the numbers given in the arrangement are two digit numbers).
Input: gone over 35 69 test 72 park 27
Step I: 27 gone over 35 69 test 72 park
Step II: 27 test gone over 35 69 72 park
Step III: 27 test 35 gone over 69 72 park
Step IV: 27 test 35 park gone over 69 72
Step V: 27 test 35 park 69 gone over 72
Step VI: 27 test 35 park 69 over gone 73
Step VII: 27 test 35 park 69 over 72 gone
And Step VII is the last step of rearrangement of the above input as the desired arrangement is obtained.
As per the rules followed in the steps, find out in each of the following questions the appropriate step for the given input.

Step II of an input: 33 store 81 75 full of goods 52
Which of the following will be Step VI?

India has signed how much amount of financing agreement with the World Bank for Strive Project?

In the figure, O is the centre of the circle with radius 5 cm. If tangent OP = 13 cm and OP intersects the circle at E. Find the perimeter of the $\Delta PCD$, where CD is the tangent to the circle at E.

A circle of radius 3 crosses the centre of a square of side length 2. Find the approximate positive difference between the areas of the non-overlapping portions of the figures

Two different primes are said to equalize an integer if they are the same distance from the integer on either sides of the number line. Which integer among the following is the most highly equalized?

In a class, 50 students offered Mathematics, 42 offered Biology and 24 offered both the subjects. Find the number of students, who offer only Mathematics .

The set of values of p for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is

The remainder obtained when ${37}^{29}-36$ is divided by 29 is

Consider the experiment of throwing a die. If a multiple of $3$ comes up, throw the die again and if any other number comes, toss a coin. The conditional probability of the event 'the coin shows a tail', given that 'atleast one die shows a $3$'.

Statements:
F $\ast$ M, M % R, E F
Conclusions:
I. M % E
II. R E

How many pen drives did Cyrus sell in the month of March?

For what values of x will the following inequality hold true $3|a-1|+a^2-7>0$ ?

Divide yourselves into groups and collect information on the use of computers from five students each of classes VI, IX and XI. Compile and summarise your answers to the questions above in the following table.

How many pairs of positive integers (a, b) are there such that a and b have no common factor greater than 1 and $\frac{a}{b}+\frac{14b}{9a}$ is an integer?

A beats B by 150 m in a race of 1000 m. B beats C by 100 m in a 1200m race. Approx by how many meters can A beat C in a race of 500 m?

Millet varieties developed through breeding are

Given that ${10}^{0.48}=x,{10}^{0.70}=yand{x}^z=y^2,$then the value of z is close to :

Study the following graph carefully and answer the questions that follow.

Q49. How many more medals should India win to make the ratio of medals won by China to India as 2:3?

When two dice are thrown simultaneously ,the probability of getting a sum of 12 is___